A steam turbine operates between hot and cold reservoir temperatures of 538.0 ¢XC and 92.1 ¢XC, respectively. If heat is supplied at a rate of 238.0 MW, what maximum amount of power could the turbine deliver?
powerdelivered=input power*thermal eff
= 238* (inlettemp-outlettemp)/outlettemp
put temps in an absolute scale, Kelvins would be convenient.
ERROR. INlettemp goes in the denominator. A brain freeze.
To determine the maximum amount of power a steam turbine can deliver, we can make use of the Carnot efficiency formula. The Carnot efficiency applies to any heat engine operating between two temperatures and is given by:
η = 1 - (Tc/Th)
Where:
η represents the Carnot efficiency,
Tc is the absolute temperature of the cold reservoir, and
Th is the absolute temperature of the hot reservoir.
To calculate the Carnot efficiency, we need to convert the temperatures from degrees Celsius (°C) to Kelvin (K) by adding 273.15:
Th = 538.0 °C + 273.15 = 811.15 K
Tc = 92.1 °C + 273.15 = 365.25 K
Now we can substitute the values into the Carnot efficiency formula:
η = 1 - (365.25 K / 811.15 K)
Calculating this, we find:
η ≈ 0.5491
The Carnot efficiency represents the ratio of the work output to the heat input. Thus, the maximum amount of power (P) the steam turbine can deliver is given by multiplying the heat input rate (Q) by the Carnot efficiency:
P = Q × η
However, we need to convert the heat input rate from MW to W, by multiplying by 10^6:
Q = 238.0 MW × 10^6 = 238,000,000 W
Now we can calculate the maximum power output (P):
P = 238,000,000 W × 0.5491 = 130,957,800 W
Therefore, the maximum amount of power the turbine could deliver is approximately 130.96 MW.